On lower transcendence degree
type: Item
instance of: scholarly article
title: On lower transcendence degree
zbMATH Open document ID: 0924.16015
author: J. J. Zhang
published in: Advances in Mathematics
publication date: 1999-09-15T00:00:00Z
review text: Recent developments in noncommutative algebraic geometry suggest that we need an invariant analogous to the transcendence degree of a field for division algebras not necessarily finite over their centers. Such an invariant is the Gelfand-Kirillov transcendence degree, denoted by Tdeg. The author defines for arbitrary associative algebras another such invariant, called the lower transcendence degree, denoted by Ld. The basic properties of Ld are established, and induction, faithful flatness and deformation theory are used to compute Ld. It is proved that \(\text{Ld}=\text{Tdeg}\) for various division algebras. Finally, Ld is used to study some open problems.
Mathematics Subject Classification ID: 16P90
Mathematics Subject Classification ID: 16K40
zbMATH DE Number: 1236400
zbMATH Keywords: Gelfand-Kirillov transcendence degree
zbMATH Keywords: division algebras
zbMATH Keywords: Ore domains
zbMATH Keywords: PI algebras
zbMATH Keywords: Artin-Schelter regular algebras
zbMATH Keywords: Weyl algebras
zbMATH Keywords: universal enveloping algebras
zbMATH Keywords: Gelfand-Kirillov dimension
reviewed by: Constantin Năstăsescu
MaRDI profile type: Publication
full work available at URL: aima.1998.1749
OpenAlex ID: W1977597787
Wikidata QID: Q107732722
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DOI: 10.1006/AIMA.1998.1749
description: scientific article; zbMATH DE number 1236400